Walkthrough

Paarthurnax reveals that Dragonsreach in Whiterun was built initially to hold other dragons. His idea is to capture one of Alduin's ilk and convince the captive to betray Alduin. Before that happens, however, you will need to convince Jarl of Whiterun first.

Jarl Balgruuf (or whoever is in his place following the events of the Civil War) fully comprehends the threat of the World-Eater looming over him like a dark shadow, an even greater threat -- the clash between the Stormcloaks and Imperial Legion -- perturbs him even more. So, if you have not already done some part of the Civil War Quests, the quest Season Unending begins, during which you are to negotiate a peace council to help suspend the civil strife while the dragons are taken cared of.

Glitch: If you are in the middle of the Civil War Quests and have chosen a side when Season Unending begins, there's a chance that you might encounter a glitch in which you can not proceed with either the Civil War quest or negotiating the truce. It is best that you finish Battle For Whiterun before you speak with the Jarl.

Using Call Dragon at the end of the balcony will call this dragon down. As the dragon enters, he will pick up the guard, leaving just the sword and torch behind. From here this quest is really simple. Whenever you get the chance, hit the dragon with Dragonrend and run inside the large opening. The dragon will land on the balcony and follow you in and be captured by the trap waiting above.